diff --git a/DESCRIPTION b/DESCRIPTION
index 901986976..8f9386320 100644
--- a/DESCRIPTION
+++ b/DESCRIPTION
@@ -1,8 +1,8 @@
Package: NNS
Type: Package
Title: Nonlinear Nonparametric Statistics
-Version: 10.9.3
-Date: 2024-10-14
+Version: 10.9.4
+Date: 2024-12-02
Authors@R: c(
person("Fred", "Viole", role=c("aut","cre"), email="ovvo.financial.systems@gmail.com"),
person("Roberto", "Spadim", role=c("ctb"))
diff --git a/NNS_10.9.3.tar.gz b/NNS_10.9.3.tar.gz
deleted file mode 100644
index 1bbd275c9..000000000
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diff --git a/NNS_10.9.3.zip b/NNS_10.9.3.zip
deleted file mode 100644
index fc6e273fa..000000000
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diff --git a/NNS_10.9.4.tar.gz b/NNS_10.9.4.tar.gz
new file mode 100644
index 000000000..68290eacb
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diff --git a/NNS_10.9.4.zip b/NNS_10.9.4.zip
new file mode 100644
index 000000000..b4e9adda2
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diff --git a/R/NNS_MC.R b/R/NNS_MC.R
index 34758e5ee..a34637c2e 100644
--- a/R/NNS_MC.R
+++ b/R/NNS_MC.R
@@ -9,7 +9,8 @@
#' @param by numeric; \code{.01} default will set the \code{by} argument in \code{seq(-1, 1, step)}.
#' @param exp numeric; \code{1} default will exponentially weight maximum rho value if \code{exp > 1}. Shrinks values towards \code{upper_rho}.
#' @param type options("spearman", "pearson", "NNScor", "NNSdep"); \code{type = "spearman"}(default) dependence metric desired.
-#' @param drift logical; \code{TRUE} default preserves the drift of the original series.
+#' @param drift logical; \code{drift = TRUE} (default) preserves the drift of the original series.
+#' @param target_drift numerical; code{NULL} (default) Specifies the desired drift when \code{drift = TRUE}, i.e. a risk-free rate of return.
#' @param xmin numeric; the lower limit for the left tail.
#' @param xmax numeric; the upper limit for the right tail.
#' @param ... possible additional arguments to be passed to \link{NNS.meboot}.
@@ -38,6 +39,7 @@ NNS.MC <- function(x,
exp = 1,
type = "spearman",
drift = TRUE,
+ target_drift = NULL,
xmin = NULL,
xmax = NULL, ...){
@@ -51,8 +53,8 @@ NNS.MC <- function(x,
exp_rhos <- rev(c((neg_rhos^exp)*-1, pos_rhos^(1/exp)))
- samples <- suppressWarnings(NNS.meboot(x = x, reps = reps, rho = exp_rhos, type = type, drift = drift,
- xmin = xmin, xmax = xmax, ...))
+ samples <- suppressWarnings(NNS.meboot(x = x, reps = reps, rho = exp_rhos, type = type,
+ drift = drift, target_drift = target_drift, xmin = xmin, xmax = xmax, ...))
replicates <- samples["replicates",]
diff --git a/R/NNS_meboot.R b/R/NNS_meboot.R
index f04d3fa69..cd0233884 100644
--- a/R/NNS_meboot.R
+++ b/R/NNS_meboot.R
@@ -6,14 +6,15 @@
#' @param reps numeric; number of replicates to generate.
#' @param rho numeric [-1,1] (vectorized); A \code{rho} must be provided, otherwise a blank list will be returned.
#' @param type options("spearman", "pearson", "NNScor", "NNSdep"); \code{type = "spearman"}(default) dependence metric desired.
-#' @param drift logical; \code{TRUE} default preserves the drift of the original series.
-#' @param trim numeric [0,1]; The mean trimming proportion, defaults to \code{trim=0.1}.
+#' @param drift logical; \code{drift = TRUE} (default) preserves the drift of the original series.
+#' @param target_drift numerical; code{NULL} (default) Specifies the desired drift when \code{drift = TRUE}, i.e. a risk-free rate of return.
+#' @param trim numeric [0,1]; The mean trimming proportion, defaults to \code{trim = 0.1}.
#' @param xmin numeric; the lower limit for the left tail.
#' @param xmax numeric; the upper limit for the right tail.
#' @param reachbnd logical; If \code{TRUE} potentially reached bounds (xmin = smallest value - trimmed mean and
#' xmax = largest value + trimmed mean) are given when the random draw happens to be equal to 0 and 1, respectively.
-#' @param expand.sd logical; If \code{TRUE} the standard deviation in the ensemble is expanded. See \code{expand.sd} in meboot::meboot.
-#' @param force.clt logical; If \code{TRUE} the ensemble is forced to satisfy the central limit theorem. See \code{force.clt} in meboot::meboot.
+#' @param expand.sd logical; If \code{TRUE} the standard deviation in the ensemble is expanded. See \code{expand.sd} in \code{meboot::meboot}.
+#' @param force.clt logical; If \code{TRUE} the ensemble is forced to satisfy the central limit theorem. See \code{force.clt} in \code{meboot::meboot}.
#' @param scl.adjustment logical; If \code{TRUE} scale adjustment is performed to ensure that the population variance of the transformed series equals the variance of the data.
#' @param sym logical; If \code{TRUE} an adjustment is performed to ensure that the ME density is symmetric.
#' @param elaps logical; If \code{TRUE} elapsed time during computations is displayed.
@@ -59,27 +60,28 @@
#' boots <- NNS.meboot(AirPassengers, reps=100, rho = 0, xmin = 0)
#'
#' # Verify correlation of replicates ensemble to original
-#' cor(boots["ensemble",], AirPassengers, method = "spearman")
+#' cor(boots["ensemble",]$ensemble, AirPassengers, method = "spearman")
#'
#' # Plot all replicates
-#' matplot(boots["replicates",] , type = 'l')
+#' matplot(boots["replicates",]$replicates , type = 'l')
#'
#' # Plot ensemble
-#' lines(boots["ensemble",], lwd = 3)
+#' lines(boots["ensemble",]$ensemble, lwd = 3)
#' }
#' @export
NNS.meboot <- function(x,
- reps=999,
- rho=NULL,
- type="spearman",
- drift=TRUE,
- trim=0.10,
- xmin=NULL,
- xmax=NULL,
- reachbnd=TRUE,
- expand.sd=TRUE, force.clt=TRUE,
- scl.adjustment = FALSE, sym = FALSE, elaps=FALSE,
+ reps = 999,
+ rho = NULL,
+ type = "spearman",
+ drift = TRUE,
+ target_drift = NULL,
+ trim = 0.10,
+ xmin = NULL,
+ xmax = NULL,
+ reachbnd = TRUE,
+ expand.sd = TRUE, force.clt = TRUE,
+ scl.adjustment = FALSE, sym = FALSE, elaps = FALSE,
digits = 6,
colsubj, coldata, coltimes,...)
{
@@ -206,47 +208,48 @@
m <- c(matrix2)
l <- length(e)
- func <- function(ab, d=drift, ty=type){
+ func <- function(ab, d = drift, ty = type) {
a <- ab[1]
b <- ab[2]
-
- if(ty=="spearman" || ty=="pearson"){
- ifelse(d,
- (abs(cor((a*m + b*e)/(a + b), e, method = ty) - rho) +
- abs(mean((a*m + b*e))/mean(e) - 1) +
- abs( cor((a*m + b*e)/(a + b), 1:l) - cor(e, 1:l))
- ),
- abs(cor((a*m + b*e)/(a + b), e, method = ty) - rho) +
- abs(mean((a*m + b*e))/mean(e) - 1)
- )
+
+ # Compute the adjusted ensemble
+ combined <- (a * m + b * e) / (a + b)
+
+ # Check correlation or dependence structure
+ if (ty == "spearman" || ty == "pearson") {
+ error <- abs(cor(combined, e, method = ty) - rho)
+ } else if (ty == "nnsdep") {
+ error <- abs(NNS.dep(combined, e)$Dependence - rho)
} else {
- if(ty=="nnsdep"){
- ifelse(d,
- (abs(NNS.dep((a*m + b*e)/(a + b), e)$Dependence - rho) +
- abs(mean((a*m + b*e))/mean(e) - 1) +
- abs( NNS.dep((a*m + b*e)/(a + b), 1:l)$Dependence - NNS.dep(e, 1:l)$Dependence)
- ),
- abs(NNS.dep((a*m + b*e)/(a + b), e)$Dependence - rho) +
- abs(mean((a*m + b*e))/mean(e) - 1)
- )
- } else {
- ifelse(d,
- (abs(NNS.dep((a*m + b*e)/(a + b), e)$Correlation - rho) +
- abs(mean((a*m + b*e))/mean(e) - 1) +
- abs( NNS.dep((a*m + b*e)/(a + b), 1:l)$Correlation - NNS.dep(e, 1:l)$Correlation)
- ),
- abs(NNS.dep((a*m + b*e)/(a + b), e)$Correlation - rho) +
- abs(mean((a*m + b*e))/mean(e) - 1)
- )
- }
+ error <- abs(NNS.dep(combined, e)$Correlation - rho)
}
+ return(error)
}
-
+
res <- optim(c(.01,.01), func, control=list(abstol = .01))
ensemble <- (res$par[1]*matrix2 + res$par[2]*ensemble) / (sum(abs(res$par)))
+
+
+ # Drift
+ orig_coef <- fast_lm(1:n, x)$coef
+ orig_intercept <- orig_coef[1]
+ orig_drift <- orig_coef[2]
+
+ new_coef <- apply(ensemble, 2, function(i) fast_lm(1:n, i)$coef)
+ slopes <- new_coef[2,]
+
+ if(drift){
+ if(is.null(target_drift)) new_slopes <- (orig_drift - slopes) else new_slopes <- (target_drift - slopes)
+ ensemble <- ensemble + t(t(sapply(new_slopes, function(slope) cumsum(rep(slope, n)))))
+
+ new_intercepts <- orig_intercept - new_coef[1,]
+ ensemble <- sweep(ensemble, 2, new_intercepts, FUN = "+")
+ }
+
+
if(identical(ordxx_2, ordxx)){
if(reps>1) ensemble <- t(apply(ensemble, 1, function(x) sample(x, size = reps, replace = TRUE)))
@@ -257,6 +260,8 @@
if(expand.sd) ensemble <- NNS.meboot.expand.sd(x=x, ensemble=ensemble, ...)
if(force.clt && reps > 1) ensemble <- force.clt(x=x, ensemble=ensemble)
+
+
# scale adjustment
@@ -279,6 +284,9 @@
# Force min / max values
if(!is.null(trim[[2]])) ensemble <- apply(ensemble, 2, function(z) pmax(trim[[2]], z))
if(!is.null(trim[[3]])) ensemble <- apply(ensemble, 2, function(z) pmin(trim[[3]], z))
+
+
+
if(is.ts(x)){
ensemble <- ts(ensemble, frequency=frequency(x), start=start(x))
@@ -287,7 +295,8 @@
if(reps>1) dimnames(ensemble)[[2]] <- paste("Replicate", 1:reps)
}
-
+
+
final <- list(x=x, replicates=round(ensemble, digits = digits), ensemble=Rfast::rowmeans(ensemble), xx=xx, z=z, dv=dv, dvtrim=dvtrim, xmin=xmin,
xmax=xmax, desintxb=desintxb, ordxx=ordxx, kappa = kappa)
diff --git a/R/Normalization.R b/R/Normalization.R
index ac729768c..5c4eff921 100644
--- a/R/Normalization.R
+++ b/R/Normalization.R
@@ -14,7 +14,7 @@
#' @examples
#' \dontrun{
#' set.seed(123)
-#' x <- rnorm(100) ; y<-rnorm(100)
+#' x <- rnorm(100) ; y <- rnorm(100)
#' A <- cbind(x, y)
#' NNS.norm(A)
#'
diff --git a/R/RcppExports.R b/R/RcppExports.R
index d8ec77493..f56b6211a 100644
--- a/R/RcppExports.R
+++ b/R/RcppExports.R
@@ -18,8 +18,7 @@ fast_lm_mult <- function(x, y) {
#' @param variable a numeric vector. \link{data.frame} or \link{list} type objects are not permissible.
#' @return LPM of variable
#' @author Fred Viole, OVVO Financial Systems
-#' @references Viole, F. and Nawrocki, D. (2013) "Nonlinear Nonparametric Statistics: Using Partial Moments"
-#' \url{https://www.amazon.com/dp/1490523995/ref=cm_sw_su_dp}
+#' @references Viole, F. and Nawrocki, D. (2013) "Nonlinear Nonparametric Statistics: Using Partial Moments" (ISBN: 1490523995)
#' @examples
#' set.seed(123)
#' x <- rnorm(100)
@@ -37,8 +36,7 @@ LPM <- function(degree, target, variable) {
#' @param variable a numeric vector. \link{data.frame} or \link{list} type objects are not permissible.
#' @return UPM of variable
#' @author Fred Viole, OVVO Financial Systems
-#' @references Viole, F. and Nawrocki, D. (2013) "Nonlinear Nonparametric Statistics: Using Partial Moments"
-#' \url{https://www.amazon.com/dp/1490523995/ref=cm_sw_su_dp}
+#' @references Viole, F. and Nawrocki, D. (2013) "Nonlinear Nonparametric Statistics: Using Partial Moments" (ISBN: 1490523995)
#' @examples
#' set.seed(123)
#' x <- rnorm(100)
@@ -56,10 +54,8 @@ UPM <- function(degree, target, variable) {
#' @param variable a numeric vector.
#' @return Standardized LPM of variable
#' @author Fred Viole, OVVO Financial Systems
-#' @references Viole, F. and Nawrocki, D. (2013) "Nonlinear Nonparametric Statistics: Using Partial Moments"
-#' \url{https://www.amazon.com/dp/1490523995/ref=cm_sw_su_dp}
-#' @references Viole, F. (2017) "Continuous CDFs and ANOVA with NNS"
-#' \url{https://www.ssrn.com/abstract=3007373}
+#' @references Viole, F. and Nawrocki, D. (2013) "Nonlinear Nonparametric Statistics: Using Partial Moments" (ISBN: 1490523995)
+#' @references Viole, F. (2017) "Continuous CDFs and ANOVA with NNS" \doi{10.2139/ssrn.3007373}
#' @examples
#' set.seed(123)
#' x <- rnorm(100)
@@ -92,8 +88,7 @@ LPM.ratio <- function(degree, target, variable) {
#' @param variable a numeric vector.
#' @return Standardized UPM of variable
#' @author Fred Viole, OVVO Financial Systems
-#' @references Viole, F. and Nawrocki, D. (2013) "Nonlinear Nonparametric Statistics: Using Partial Moments"
-#' \url{https://www.amazon.com/dp/1490523995/ref=cm_sw_su_dp}
+#' @references Viole, F. and Nawrocki, D. (2013) "Nonlinear Nonparametric Statistics: Using Partial Moments" (ISBN: 1490523995)
#' @examples
#' set.seed(123)
#' x <- rnorm(100)
@@ -121,8 +116,7 @@ UPM.ratio <- function(degree, target, variable) {
#' @param target_y numeric; Target for lower deviations of variable Y. Typically the mean of Variable Y for classical statistics equivalences, but does not have to be.
#' @return Co-LPM of two variables
#' @author Fred Viole, OVVO Financial Systems
-#' @references Viole, F. and Nawrocki, D. (2013) "Nonlinear Nonparametric Statistics: Using Partial Moments"
-#' \url{https://www.amazon.com/dp/1490523995/ref=cm_sw_su_dp}
+#' @references Viole, F. and Nawrocki, D. (2013) "Nonlinear Nonparametric Statistics: Using Partial Moments" (ISBN: 1490523995)
#' @examples
#' set.seed(123)
#' x <- rnorm(100) ; y <- rnorm(100)
@@ -143,8 +137,7 @@ Co.LPM <- function(degree_lpm, x, y, target_x, target_y) {
#' @param target_y numeric; Target for upside deviations of variable Y. Typically the mean of Variable Y for classical statistics equivalences, but does not have to be.
#' @return Co-UPM of two variables
#' @author Fred Viole, OVVO Financial Systems
-#' @references Viole, F. and Nawrocki, D. (2013) "Nonlinear Nonparametric Statistics: Using Partial Moments"
-#' \url{https://www.amazon.com/dp/1490523995/ref=cm_sw_su_dp}
+#' @references Viole, F. and Nawrocki, D. (2013) "Nonlinear Nonparametric Statistics: Using Partial Moments" (ISBN: 1490523995)
#' @examples
#' set.seed(123)
#' x <- rnorm(100) ; y <- rnorm(100)
@@ -166,8 +159,7 @@ Co.UPM <- function(degree_upm, x, y, target_x, target_y) {
#' @param target_y numeric; Target for lower deviations of variable Y. Typically the mean of Variable Y for classical statistics equivalences, but does not have to be.
#' @return Divergent LPM of two variables
#' @author Fred Viole, OVVO Financial Systems
-#' @references Viole, F. and Nawrocki, D. (2013) "Nonlinear Nonparametric Statistics: Using Partial Moments"
-#' \url{https://www.amazon.com/dp/1490523995/ref=cm_sw_su_dp}
+#' @references Viole, F. and Nawrocki, D. (2013) "Nonlinear Nonparametric Statistics: Using Partial Moments" (ISBN: 1490523995)
#' @examples
#' set.seed(123)
#' x <- rnorm(100) ; y <- rnorm(100)
@@ -189,8 +181,7 @@ D.LPM <- function(degree_lpm, degree_upm, x, y, target_x, target_y) {
#' @param target_y numeric; Target for upper deviations of variable Y. Typically the mean of Variable Y for classical statistics equivalences, but does not have to be.
#' @return Divergent UPM of two variables
#' @author Fred Viole, OVVO Financial Systems
-#' @references Viole, F. and Nawrocki, D. (2013) "Nonlinear Nonparametric Statistics: Using Partial Moments"
-#' \url{https://www.amazon.com/dp/1490523995/ref=cm_sw_su_dp}
+#' @references Viole, F. and Nawrocki, D. (2013) "Nonlinear Nonparametric Statistics: Using Partial Moments" (ISBN: 1490523995)
#' @examples
#' set.seed(123)
#' x <- rnorm(100) ; y <- rnorm(100)
@@ -212,10 +203,8 @@ D.UPM <- function(degree_lpm, degree_upm, x, y, target_x, target_y) {
#' @return Matrix of partial moment quadrant values (CUPM, DUPM, DLPM, CLPM), and overall covariance matrix. Uncalled quadrants will return a matrix of zeros.
#' @note For divergent asymmetical \code{"D.LPM" and "D.UPM"} matrices, matrix is \code{D.LPM(column,row,...)}.
#' @author Fred Viole, OVVO Financial Systems
-#' @references Viole, F. and Nawrocki, D. (2013) "Nonlinear Nonparametric Statistics: Using Partial Moments"
-#' \url{https://www.amazon.com/dp/1490523995/ref=cm_sw_su_dp}
-#' @references Viole, F. (2017) "Bayes' Theorem From Partial Moments"
-#' \url{https://www.ssrn.com/abstract=3457377}
+#' @references Viole, F. and Nawrocki, D. (2013) "Nonlinear Nonparametric Statistics: Using Partial Moments" (ISBN: 1490523995)
+#' @references Viole, F. (2017) "Bayes' Theorem From Partial Moments" \doi{10.2139/ssrn.3457377}
#' @examples
#' set.seed(123)
#' x <- rnorm(100) ; y <- rnorm(100) ; z <- rnorm(100)
diff --git a/README.md b/README.md
index 0c14efb9b..eb2586b5a 100644
--- a/README.md
+++ b/README.md
@@ -3,7 +3,7 @@
-[](https://github.com/OVVO-Financial/NNS/commits/NNS-Beta-Version) [](https://www.gnu.org/licenses/gpl-3.0.en.html)
+[](https://github.com/OVVO-Financial/NNS/commits/NNS-Beta-Version) [](https://www.gnu.org/licenses/gpl-3.0.en.html)
@@ -59,7 +59,7 @@ Please see https://github.com/OVVO-Financial/NNS/blob/NNS-Beta-Version/examples/
title = {NNS: Nonlinear Nonparametric Statistics},
author = {Fred Viole},
year = {2016},
- note = {R package version 10.9.3},
+ note = {R package version 10.9.4},
url = {https://CRAN.R-project.org/package=NNS},
}
```
diff --git a/doc/NNSvignette_Sampling.R b/doc/NNSvignette_Sampling.R
index 87976c6b1..d16bc8028 100644
--- a/doc/NNSvignette_Sampling.R
+++ b/doc/NNSvignette_Sampling.R
@@ -149,7 +149,7 @@ legend('left', legend = c('ecdf', 'LPM.ratio'), fill=c('black','red'), border=NA
# sapply(boots, function(r) cor(r, x, method = "spearman"))
#
# rho = 1 rho = 0.5 rho = -0.5 rho = -1
-# 1.0000000 0.4988059 -0.4995740 -0.9982358
+# 1.0000000 0.4989619 -0.4984818 -0.9779778
## ----multisim, eval=FALSE-----------------------------------------------------
# set.seed(123)
@@ -171,8 +171,8 @@ legend('left', legend = c('ecdf', 'LPM.ratio'), fill=c('black','red'), border=NA
# NNS.copula(original.data)
# NNS.copula(new.dep.data)
#
-# [1] 0.4379469
-# [1] 0.4390599
+# [1] 0.4353849
+# [1] 0.4357026
## ----eval=FALSE---------------------------------------------------------------
# head(original.data)
@@ -206,17 +206,17 @@ legend('left', legend = c('ecdf', 'LPM.ratio'), fill=c('black','red'), border=NA
## ----eval=FALSE---------------------------------------------------------------
# for(i in 1:4) print(cor(new.boot.dep.matrix[,i], original.data[,i], method = "spearman"))
#
-# [1] 0.9453275
-# [1] 0.9523726
-# [1] 0.9498499
-# [1] 0.9524516
+# [1] 0.9432899
+# [1] 0.9460947
+# [1] 0.9442031
+# [1] 0.9423242
## ----eval=FALSE---------------------------------------------------------------
# NNS.copula(original.data)
# NNS.copula(new.boot.dep.matrix)
#
-# [1] 0.4379469
-# [1] 0.4302545
+# [1] 0.4353849
+# [1] 0.4263725
## ----eval=FALSE---------------------------------------------------------------
# head(original.data)
@@ -230,12 +230,12 @@ legend('left', legend = c('ecdf', 'LPM.ratio'), fill=c('black','red'), border=NA
# [5,] 0.12928774 -2.54934277 0.1741359 0.12928774
# [6,] 1.71506499 1.04057346 -0.6152683 1.71506499
# x y z x
-# ensemble1 -0.4667731 -0.8418413 -0.6139059 -0.4708890
-# ensemble2 -0.2333747 -1.0908710 0.3748315 -0.2711240
-# ensemble3 1.4799734 0.2893831 -0.3851513 1.3645317
-# ensemble4 0.1751654 0.2995113 1.1342461 0.1486429
-# ensemble5 0.4128802 -2.9789634 -0.1141124 0.3846150
-# ensemble6 1.5592660 1.1800553 -0.5285532 1.5041917
+# ensemble1 -0.4268047 -0.7794553 -0.6364458 -0.4642642
+# ensemble2 -0.2965744 -1.0682197 0.3297265 -0.2531178
+# ensemble3 1.3302149 0.3054734 -0.4014515 1.4914884
+# ensemble4 0.2257378 0.3108846 1.0603892 0.1728540
+# ensemble5 0.4716743 -3.3344967 -0.1917697 0.4309379
+# ensemble6 1.3984978 1.1881374 -0.5295386 1.5326055
## ----threads, echo = FALSE----------------------------------------------------
Sys.setenv("OMP_THREAD_LIMIT" = "")
diff --git a/doc/NNSvignette_Sampling.Rmd b/doc/NNSvignette_Sampling.Rmd
index 380b3028f..0e559a0a5 100644
--- a/doc/NNSvignette_Sampling.Rmd
+++ b/doc/NNSvignette_Sampling.Rmd
@@ -224,7 +224,7 @@ Checking our replicate correlations:
sapply(boots, function(r) cor(r, x, method = "spearman"))
rho = 1 rho = 0.5 rho = -0.5 rho = -1
- 1.0000000 0.4988059 -0.4995740 -0.9982358
+ 1.0000000 0.4989619 -0.4984818 -0.9779778
```
More replicates and ensembles thereof can be generated for any number of $\rho$ values. Please see the full **`NNS.meboot`** and **`NNS.MC`** argument documentation.
@@ -270,8 +270,8 @@ Similar dependence with radically different values, since we used $N(10, 20)$ in
NNS.copula(original.data)
NNS.copula(new.dep.data)
-[1] 0.4379469
-[1] 0.4390599
+[1] 0.4353849
+[1] 0.4357026
```
```{r, eval=FALSE}
@@ -316,10 +316,10 @@ Checking `ensemble` correlations with `original.data`:
```{r, eval=FALSE}
for(i in 1:4) print(cor(new.boot.dep.matrix[,i], original.data[,i], method = "spearman"))
-[1] 0.9453275
-[1] 0.9523726
-[1] 0.9498499
-[1] 0.9524516
+[1] 0.9432899
+[1] 0.9460947
+[1] 0.9442031
+[1] 0.9423242
```
### Compare Multivariate Dependence Structures
@@ -330,8 +330,8 @@ Similar dependence with similar values.
NNS.copula(original.data)
NNS.copula(new.boot.dep.matrix)
-[1] 0.4379469
-[1] 0.4302545
+[1] 0.4353849
+[1] 0.4263725
```
```{r, eval=FALSE}
@@ -346,12 +346,12 @@ head(new.boot.dep.matrix)
[5,] 0.12928774 -2.54934277 0.1741359 0.12928774
[6,] 1.71506499 1.04057346 -0.6152683 1.71506499
x y z x
-ensemble1 -0.4667731 -0.8418413 -0.6139059 -0.4708890
-ensemble2 -0.2333747 -1.0908710 0.3748315 -0.2711240
-ensemble3 1.4799734 0.2893831 -0.3851513 1.3645317
-ensemble4 0.1751654 0.2995113 1.1342461 0.1486429
-ensemble5 0.4128802 -2.9789634 -0.1141124 0.3846150
-ensemble6 1.5592660 1.1800553 -0.5285532 1.5041917
+ensemble1 -0.4268047 -0.7794553 -0.6364458 -0.4642642
+ensemble2 -0.2965744 -1.0682197 0.3297265 -0.2531178
+ensemble3 1.3302149 0.3054734 -0.4014515 1.4914884
+ensemble4 0.2257378 0.3108846 1.0603892 0.1728540
+ensemble5 0.4716743 -3.3344967 -0.1917697 0.4309379
+ensemble6 1.3984978 1.1881374 -0.5295386 1.5326055
```
# References {#references}
diff --git a/doc/NNSvignette_Sampling.html b/doc/NNSvignette_Sampling.html
index 2089ea982..03b30c4db 100644
--- a/doc/NNSvignette_Sampling.html
+++ b/doc/NNSvignette_Sampling.html
@@ -471,12 +471,12 @@ Bootstrapping (NNS.meboot)
plot(x, type = "l", lwd = 3, ylim = c(min(reps), max(reps)))
matplot(reps, type = "l", col = rainbow(length(boots)), add = TRUE)
-
+
Checking our replicate correlations:
sapply(boots, function(r) cor(r, x, method = "spearman"))
rho = 1 rho = 0.5 rho = -0.5 rho = -1
- 1.0000000 0.4988059 -0.4995740 -0.9982358
More replicates and ensembles thereof can be generated for any number
of \(\rho\) values. Please see the full
NNS.meboot and
@@ -531,8 +531,8 @@
Compare Multivariate Dependence Structures
NNS.copula(original.data)
NNS.copula(new.dep.data)
-[1] 0.4379469
-[1] 0.4390599
head(original.data)
head(new.dep.data)
@@ -572,18 +572,18 @@ Alternative Using NNS.meboot
original.data:
for(i in 1:4) print(cor(new.boot.dep.matrix[,i], original.data[,i], method = "spearman"))
-[1] 0.9453275
-[1] 0.9523726
-[1] 0.9498499
-[1] 0.9524516
Compare Multivariate Dependence Structures
Similar dependence with similar values.
NNS.copula(original.data)
NNS.copula(new.boot.dep.matrix)
-[1] 0.4379469
-[1] 0.4302545
+
[1] 0.4353849
+
[1] 0.4263725
head(original.data)
head(new.boot.dep.matrix)
@@ -595,12 +595,12 @@ Compare Multivariate Dependence Structures
[5,] 0.12928774 -2.54934277 0.1741359 0.12928774
[6,] 1.71506499 1.04057346 -0.6152683 1.71506499
x y z x
-ensemble1 -0.4667731 -0.8418413 -0.6139059 -0.4708890
-ensemble2 -0.2333747 -1.0908710 0.3748315 -0.2711240
-ensemble3 1.4799734 0.2893831 -0.3851513 1.3645317
-ensemble4 0.1751654 0.2995113 1.1342461 0.1486429
-ensemble5 0.4128802 -2.9789634 -0.1141124 0.3846150
-ensemble6 1.5592660 1.1800553 -0.5285532 1.5041917
NNS Partitions
## 15: 5.800000 3.619048 4.383333 1.800000
## 16: 5.983333 3.800000 4.500000 1.900000
## 17: 6.100000 3.900000 4.600000 2.000000
-## 18: 6.200000 4.200000 4.700000 2.114583
+## 18: 6.200000 4.137305 4.700000 2.114583
## 19: 6.300000 4.400000 4.863889 2.300000
## 20: 6.400000 NA 5.000000 2.433333
## 21: 6.500000 NA 5.100000 2.500000
@@ -405,8 +405,8 @@ NNS Partitions
## 23: 6.700000 NA 5.333333 NA
## 24: 6.864286 NA 5.500000 NA
## 25: 7.153750 NA 5.614583 NA
-## 26: 7.400000 NA 5.929049 NA
-## 27: 7.710000 NA 6.612109 NA
+## 26: 7.400000 NA 5.924883 NA
+## 27: 7.710000 NA 6.607943 NA
## 28: 7.900000 NA 6.900000 NA
## V1 V2 V3 V4
diff --git a/vignettes/NNSvignette_Clustering_and_Regression.html b/vignettes/NNSvignette_Clustering_and_Regression.html
index 7819aa4c8..38d0b35a7 100644
--- a/vignettes/NNSvignette_Clustering_and_Regression.html
+++ b/vignettes/NNSvignette_Clustering_and_Regression.html
@@ -366,7 +366,7 @@ NNS Partitioning NNS.part()
x = seq(-5, 5, .05); y = x ^ 3
for(i in 1 : 4){NNS.part(x, y, order = i, Voronoi = TRUE, obs.req = 0)}
+
X-only Partitioning
NNS.part offers a partitioning based on
@@ -375,7 +375,7 @@
X-only Partitioning
the entire bandwidth in its regression point derivation, and shares the
same limit condition as partitioning via both
\(x\) and
\(y\) values.
for(i in 1 : 4){NNS.part(x, y, order = i, type = "XONLY", Voronoi = TRUE)}
-
+
Note the partition identifications are limited to 1’s and 2’s (left
and right of the partition respectively), not the 4 values per the \(x\) and \(y\) partitioning.
## $order
@@ -404,7 +404,7 @@ X-only Partitioning
## 5: q211 0.5866563 0.2366875
## 6: q212 1.8366563 6.6437852
## 7: q221 3.0862812 30.1590941
-## 8: q222 4.3613732 84.1050922
+## 8: q222 4.3572065 83.8672381
@@ -413,7 +413,7 @@
Clusters Used in Regression
endpoints and central point) for the order of
NNS
partitioning.
for(i in 1 : 3){NNS.part(x, y, order = i, obs.req = 0, Voronoi = TRUE, type = "XONLY") ; NNS.reg(x, y, order = i, ncores = 1)}
-
+
@@ -693,7 +693,7 @@
Threshold
offers a method of reducing regressors further by controlling the
absolute value of required correlation.
NNS.reg(iris[ , 1 : 4], iris[ , 5], dim.red.method = "cor", threshold = .75, location = "topleft", ncores = 1)$equation
-
+
## Variable Coefficient
## 1: Sepal.Length 0.7980781
## 2: Sepal.Width 0.0000000
@@ -707,7 +707,7 @@ Threshold
the full regression above, again called with
NNS.reg(...)$Point.est.
NNS.reg(iris[ , 1 : 4], iris[ , 5], dim.red.method = "cor", threshold = .75, point.est = iris[1 : 10, 1 : 4], location = "topleft", ncores = 1)$Point.est
+
## [1] 1 1 1 1 1 1 1 1 1 1
Nonlinear Relationship
Note the fact that all observations occupy the co-partial moment
quadrants.
x = seq(0, 3, .01) ; y = x ^ 10
+
## [1] 0.6610183
@@ -394,7 +394,7 @@ Cyclic Relationship
divergent partial moment quadrants, are properly compensated for in
NNS.dep.
x = seq(0, 12*pi, pi/100) ; y = sin(x)
+
## [1] -0.1297766
@@ -404,15 +404,40 @@ Cyclic Relationship
## $Dependence
## [1] 0.8938585
+
+
Asymmetrical Analysis
+
The asymmetrical analysis is critical for further determining a
+causal path between variables which should be identifiable, i.e., it is
+asymmetrical in causes and effects.
+
The previous cyclic example visually highlights the asymmetry of
+dependence between the variables, which can be confirmed using
+NNS.dep(..., asym = TRUE).
+
+
## [1] -0.1297766
+
NNS.dep(x, y, asym = TRUE)
+
## $Correlation
+## [1] -0.0002077384
+##
+## $Dependence
+## [1] 0.8938585
+
+
## [1] -0.1297766
+
NNS.dep(y, x, asym = TRUE)
+
## $Correlation
+## [1] -0.07074914
+##
+## $Dependence
+## [1] 0.07074914
+
Dependence
Note the fact that all observations occupy only co- or divergent
partial moment quadrants for a given subquadrant.
-
set.seed(123)
-df <- data.frame(x = runif(10000, -1, 1), y = runif(10000, -1, 1))
-df <- subset(df, (x ^ 2 + y ^ 2 <= 1 & x ^ 2 + y ^ 2 >= 0.95))
-
-
+
set.seed(123)
+df <- data.frame(x = runif(10000, -1, 1), y = runif(10000, -1, 1))
+df <- subset(df, (x ^ 2 + y ^ 2 <= 1 & x ^ 2 + y ^ 2 >= 0.95))
+
+
## $Correlation
## [1] 0.05741863
##
@@ -430,30 +455,31 @@ p-values for NNS.dep()
Simply set
NNS.dep(..., p.value = TRUE, print.map = TRUE)
to run 100 permutations and plot the results.
-## p-values for [NNS.dep]
-x <- seq(-5, 5, .1); y <- x^2 + rnorm(length(x))
-NNS.dep(x, y, p.value = TRUE, print.map = TRUE)
+## p-values for [NNS.dep]
+set.seed(123)
+x <- seq(-5, 5, .1); y <- x^2 + rnorm(length(x))
+NNS.dep(x, y, p.value = TRUE, print.map = TRUE)
## $Correlation
-## [1] -0.03697032
+## [1] 0.2003584
##
## $`Correlation p.value`
-## [1] 0.23
+## [1] 0.24
##
## $`Correlation 95% CIs`
## 2.5% 97.5%
-## -0.1649756 0.3423353
+## -0.1748792 0.3783630
##
## $Dependence
-## [1] 0.8373177
+## [1] 0.8886629
##
## $`Dependence p.value`
## [1] 0
##
## $`Dependence 95% CIs`
## 2.5% 97.5%
-## 0.3414161 0.5663028
+## 0.3342770 0.5537688
Multivariate Dependence NNS.copula()
@@ -461,9 +487,9 @@
Multivariate Dependence NNS.copula()
multivariate instances and deliver a dependence measure
\((D)\) such that
\(D \in [0,1]\). This level of analysis is
simply impossible with Pearson or other rank based correlation methods,
which are restricted to bivariate cases.
-
set.seed(123)
-x <- rnorm(1000); y <- rnorm(1000); z <- rnorm(1000)
-NNS.copula(cbind(x, y, z), plot = TRUE, independence.overlay = TRUE)
+
set.seed(123)
+x <- rnorm(1000); y <- rnorm(1000); z <- rnorm(1000)
+NNS.copula(cbind(x, y, z), plot = TRUE, independence.overlay = TRUE)
## [1] 0.1231362
diff --git a/vignettes/NNSvignette_Sampling.R b/vignettes/NNSvignette_Sampling.R
index 87976c6b1..d16bc8028 100644
--- a/vignettes/NNSvignette_Sampling.R
+++ b/vignettes/NNSvignette_Sampling.R
@@ -149,7 +149,7 @@ legend('left', legend = c('ecdf', 'LPM.ratio'), fill=c('black','red'), border=NA
# sapply(boots, function(r) cor(r, x, method = "spearman"))
#
# rho = 1 rho = 0.5 rho = -0.5 rho = -1
-# 1.0000000 0.4988059 -0.4995740 -0.9982358
+# 1.0000000 0.4989619 -0.4984818 -0.9779778
## ----multisim, eval=FALSE-----------------------------------------------------
# set.seed(123)
@@ -171,8 +171,8 @@ legend('left', legend = c('ecdf', 'LPM.ratio'), fill=c('black','red'), border=NA
# NNS.copula(original.data)
# NNS.copula(new.dep.data)
#
-# [1] 0.4379469
-# [1] 0.4390599
+# [1] 0.4353849
+# [1] 0.4357026
## ----eval=FALSE---------------------------------------------------------------
# head(original.data)
@@ -206,17 +206,17 @@ legend('left', legend = c('ecdf', 'LPM.ratio'), fill=c('black','red'), border=NA
## ----eval=FALSE---------------------------------------------------------------
# for(i in 1:4) print(cor(new.boot.dep.matrix[,i], original.data[,i], method = "spearman"))
#
-# [1] 0.9453275
-# [1] 0.9523726
-# [1] 0.9498499
-# [1] 0.9524516
+# [1] 0.9432899
+# [1] 0.9460947
+# [1] 0.9442031
+# [1] 0.9423242
## ----eval=FALSE---------------------------------------------------------------
# NNS.copula(original.data)
# NNS.copula(new.boot.dep.matrix)
#
-# [1] 0.4379469
-# [1] 0.4302545
+# [1] 0.4353849
+# [1] 0.4263725
## ----eval=FALSE---------------------------------------------------------------
# head(original.data)
@@ -230,12 +230,12 @@ legend('left', legend = c('ecdf', 'LPM.ratio'), fill=c('black','red'), border=NA
# [5,] 0.12928774 -2.54934277 0.1741359 0.12928774
# [6,] 1.71506499 1.04057346 -0.6152683 1.71506499
# x y z x
-# ensemble1 -0.4667731 -0.8418413 -0.6139059 -0.4708890
-# ensemble2 -0.2333747 -1.0908710 0.3748315 -0.2711240
-# ensemble3 1.4799734 0.2893831 -0.3851513 1.3645317
-# ensemble4 0.1751654 0.2995113 1.1342461 0.1486429
-# ensemble5 0.4128802 -2.9789634 -0.1141124 0.3846150
-# ensemble6 1.5592660 1.1800553 -0.5285532 1.5041917
+# ensemble1 -0.4268047 -0.7794553 -0.6364458 -0.4642642
+# ensemble2 -0.2965744 -1.0682197 0.3297265 -0.2531178
+# ensemble3 1.3302149 0.3054734 -0.4014515 1.4914884
+# ensemble4 0.2257378 0.3108846 1.0603892 0.1728540
+# ensemble5 0.4716743 -3.3344967 -0.1917697 0.4309379
+# ensemble6 1.3984978 1.1881374 -0.5295386 1.5326055
## ----threads, echo = FALSE----------------------------------------------------
Sys.setenv("OMP_THREAD_LIMIT" = "")
diff --git a/vignettes/NNSvignette_Sampling.Rmd b/vignettes/NNSvignette_Sampling.Rmd
index 380b3028f..0e559a0a5 100644
--- a/vignettes/NNSvignette_Sampling.Rmd
+++ b/vignettes/NNSvignette_Sampling.Rmd
@@ -224,7 +224,7 @@ Checking our replicate correlations:
sapply(boots, function(r) cor(r, x, method = "spearman"))
rho = 1 rho = 0.5 rho = -0.5 rho = -1
- 1.0000000 0.4988059 -0.4995740 -0.9982358
+ 1.0000000 0.4989619 -0.4984818 -0.9779778
```
More replicates and ensembles thereof can be generated for any number of $\rho$ values. Please see the full **`NNS.meboot`** and **`NNS.MC`** argument documentation.
@@ -270,8 +270,8 @@ Similar dependence with radically different values, since we used $N(10, 20)$ in
NNS.copula(original.data)
NNS.copula(new.dep.data)
-[1] 0.4379469
-[1] 0.4390599
+[1] 0.4353849
+[1] 0.4357026
```
```{r, eval=FALSE}
@@ -316,10 +316,10 @@ Checking `ensemble` correlations with `original.data`:
```{r, eval=FALSE}
for(i in 1:4) print(cor(new.boot.dep.matrix[,i], original.data[,i], method = "spearman"))
-[1] 0.9453275
-[1] 0.9523726
-[1] 0.9498499
-[1] 0.9524516
+[1] 0.9432899
+[1] 0.9460947
+[1] 0.9442031
+[1] 0.9423242
```
### Compare Multivariate Dependence Structures
@@ -330,8 +330,8 @@ Similar dependence with similar values.
NNS.copula(original.data)
NNS.copula(new.boot.dep.matrix)
-[1] 0.4379469
-[1] 0.4302545
+[1] 0.4353849
+[1] 0.4263725
```
```{r, eval=FALSE}
@@ -346,12 +346,12 @@ head(new.boot.dep.matrix)
[5,] 0.12928774 -2.54934277 0.1741359 0.12928774
[6,] 1.71506499 1.04057346 -0.6152683 1.71506499
x y z x
-ensemble1 -0.4667731 -0.8418413 -0.6139059 -0.4708890
-ensemble2 -0.2333747 -1.0908710 0.3748315 -0.2711240
-ensemble3 1.4799734 0.2893831 -0.3851513 1.3645317
-ensemble4 0.1751654 0.2995113 1.1342461 0.1486429
-ensemble5 0.4128802 -2.9789634 -0.1141124 0.3846150
-ensemble6 1.5592660 1.1800553 -0.5285532 1.5041917
+ensemble1 -0.4268047 -0.7794553 -0.6364458 -0.4642642
+ensemble2 -0.2965744 -1.0682197 0.3297265 -0.2531178
+ensemble3 1.3302149 0.3054734 -0.4014515 1.4914884
+ensemble4 0.2257378 0.3108846 1.0603892 0.1728540
+ensemble5 0.4716743 -3.3344967 -0.1917697 0.4309379
+ensemble6 1.3984978 1.1881374 -0.5295386 1.5326055
```
# References {#references}
diff --git a/vignettes/NNSvignette_Sampling.html b/vignettes/NNSvignette_Sampling.html
index 2089ea982..03b30c4db 100644
--- a/vignettes/NNSvignette_Sampling.html
+++ b/vignettes/NNSvignette_Sampling.html
@@ -471,12 +471,12 @@
Bootstrapping (NNS.meboot)
plot(x, type = "l", lwd = 3, ylim = c(min(reps), max(reps)))
matplot(reps, type = "l", col = rainbow(length(boots)), add = TRUE)
+
Checking our replicate correlations:
sapply(boots, function(r) cor(r, x, method = "spearman"))
rho = 1 rho = 0.5 rho = -0.5 rho = -1
- 1.0000000 0.4988059 -0.4995740 -0.9982358
More replicates and ensembles thereof can be generated for any number
of \(\rho\) values. Please see the full
NNS.meboot and
@@ -531,8 +531,8 @@
Compare Multivariate Dependence Structures
NNS.copula(original.data)
NNS.copula(new.dep.data)
-[1] 0.4379469
-[1] 0.4390599
head(original.data)
head(new.dep.data)
@@ -572,18 +572,18 @@ Alternative Using NNS.meboot
original.data:
for(i in 1:4) print(cor(new.boot.dep.matrix[,i], original.data[,i], method = "spearman"))
-[1] 0.9453275
-[1] 0.9523726
-[1] 0.9498499
-[1] 0.9524516
Compare Multivariate Dependence Structures
Similar dependence with similar values.
NNS.copula(original.data)
NNS.copula(new.boot.dep.matrix)
-[1] 0.4379469
-[1] 0.4302545
+
[1] 0.4353849
+
[1] 0.4263725
head(original.data)
head(new.boot.dep.matrix)
@@ -595,12 +595,12 @@ Compare Multivariate Dependence Structures
[5,] 0.12928774 -2.54934277 0.1741359 0.12928774
[6,] 1.71506499 1.04057346 -0.6152683 1.71506499
x y z x
-ensemble1 -0.4667731 -0.8418413 -0.6139059 -0.4708890
-ensemble2 -0.2333747 -1.0908710 0.3748315 -0.2711240
-ensemble3 1.4799734 0.2893831 -0.3851513 1.3645317
-ensemble4 0.1751654 0.2995113 1.1342461 0.1486429
-ensemble5 0.4128802 -2.9789634 -0.1141124 0.3846150
-ensemble6 1.5592660 1.1800553 -0.5285532 1.5041917